A Master Equation for Screening in Luminal Horndeski Gravity
Abstract
Determining the active screening mechanism from a general scalar-tensor Lagrangian remains a challenging problem. As a diagnostic tool, we present a systematic study of nonlinear cosmological perturbations in luminal Horndeski theories. Working in the α-basis on a flat FLRW background, we derive and organise the full set of unapproximated second-order perturbation equations and systematically apply the quasistatic and weak-field limits. We find that second-order effects modify only the scalar-field equation. We derive, for static and spherically symmetric configurations, a master screening equation that classifies the nonlinear operators driving screening, recovering the Vainshtein mechanism and the onset of chameleon screening. We also identify a novel candidate regime, which we term Phaedrus screening, characterised by a screening radius that scales linearly with the source mass. For each mechanism, we derive analytical and numerical solutions and clarify the conditions under which they activate. Two new publicly available software packages are introduced: (i) xAlpha, a Mathematica package to compute and organize perturbation equations in scalar-tensor theories, and (ii) escut, a python module to solve the nonlinear scalar equation. In many cases, these tools enable the identification of the active screening type directly from a luminal Horndeski Lagrangian.
Versions
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BibTeX
@misc{sirera2026master,
title = {{A Master Equation for Screening in Luminal Horndeski Gravity}},
author = {Sergi Sirera and Tessa Baker and James Hallam and Krishna Naidoo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.04154},
eprint = {2605.04154},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.04154},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Master Equation for Screening in Luminal Horndeski Gravity
AU - Sergi Sirera
AU - Tessa Baker
AU - James Hallam
AU - Krishna Naidoo
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2605.04154
UR - https://arxiv.org/abs/2605.04154
AB - Determining the active screening mechanism from a general scalar-tensor Lagrangian remains a challenging problem. As a diagnostic tool, we present a systematic study of nonlinear cosmological perturbations in luminal Horndeski theories. Working in the α-basis on a flat FLRW background, we derive and organise the full set of unapproximated second-order perturbation equations and systematically apply the quasistatic and weak-field limits. We find that second-order effects modify only the scalar-field equation. We derive, for static and spherically symmetric configurations, a master screening equation that classifies the nonlinear operators driving screening, recovering the Vainshtein mechanism and the onset of chameleon screening. We also identify a novel candidate regime, which we term Phaedrus screening, characterised by a screening radius that scales linearly with the source mass. For each mechanism, we derive analytical and numerical solutions and clarify the conditions under which they activate. Two new publicly available software packages are introduced: (i) xAlpha, a Mathematica package to compute and organize perturbation equations in scalar-tensor theories, and (ii) escut, a python module to solve the nonlinear scalar equation. In many cases, these tools enable the identification of the active screening type directly from a luminal Horndeski Lagrangian.
ER -